This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: MATH 191, Sections 1 and 3 Calculus I Fall 2007 Section 3.2: The Product and Quotient Rules Let’s continue amassing shortcuts for computing derivatives. We’ve now got rules for differentiating powers, as well as constant multiples, sums, and dif ferences of functions whose derivatives we already know. We even know the derivative of an exponential function f ( x ) = e x ! What’s missing? Well, lots. Products, for one. Let’s examine d dx ( f · g ), and see if we can get a nice formula. Sadly, it’s not what we might immediately expect. First, a motivating Example. Consider the numbers 4 and 7, whose product is 4 · 7 = 28. What happens if we add a very small quantity, say Δ 1 , to 4, and another small quan tity, Δ 2 , to 7, and then recompute the product? We now get (4 + Δ 1 )(7 + Δ 2 ) = . This expression represents the value to which the product 4 · 7 has been changed corresponding to a small change in those values. What’s most interesting here are those two “crossterms” in the middle. If we think of 4 and 7 as the valuesare those two “crossterms” in the middle....
View
Full
Document
This note was uploaded on 04/08/2008 for the course MATH 191 taught by Professor Bahls during the Fall '07 term at UNC Asheville.
 Fall '07
 BAHLS
 Derivative, Quotient Rule

Click to edit the document details